Question

Допоможіть!!!БУДУ ВДЯЧНА!ДЯКУЮ!

Answer 1

Ответ:

Дано: $\frac{sin(\frac{\pi }{2} + \alpha) + ctg(\pi + \alpha ) }{-tg(\frac{3}{2} \pi + \alpha )} = 1 + sin\alpha$

$sin(\frac{\pi }{2} +\alpha ) = cos\alpha$

ctg(π + α) = ctgα

$-tg(\frac{3}{2} \pi +\alpha ) = ctg\alpha$

Тогда:

$\frac{cos\alpha + ctg\alpha }{ctg\alpha } = 1 + sin\alpha$

$\frac{cos\alpha }{ctg\alpha } + \frac{ctg\alpha }{ctg\alpha } = 1 + sin\alpha$

$\frac{cos\alpha }{ctg\alpha } = sin\alpha, tak \ kak \\ ctg\alpha = \frac{cos\alpha }{sin\alpha }\\\frac{cos\alpha }{\frac{cos\alpha }{sin\alpha } } = cos\alpha : \frac{cos\alpha }{sin\alpha } = cos\alpha * \frac{sin\alpha }{cos\alpha } = \bold {sin\alpha }$

$sin\alpha + \frac{ctg\alpha }{ctg\alpha } = 1 + sin\alpha$

sinα + 1 = 1 + sinα

1 + sinα = 1 + sinα.